Highest Common Factor of 960, 610, 783 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 960, 610, 783 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 960, 610, 783 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 960, 610, 783 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 960, 610, 783 is 1.

HCF(960, 610, 783) = 1

HCF of 960, 610, 783 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 960, 610, 783 is 1.

Highest Common Factor of 960,610,783 using Euclid's algorithm

Highest Common Factor of 960,610,783 is 1

Step 1: Since 960 > 610, we apply the division lemma to 960 and 610, to get

960 = 610 x 1 + 350

Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 350 and 610, to get

610 = 350 x 1 + 260

Step 3: We consider the new divisor 350 and the new remainder 260, and apply the division lemma to get

350 = 260 x 1 + 90

We consider the new divisor 260 and the new remainder 90,and apply the division lemma to get

260 = 90 x 2 + 80

We consider the new divisor 90 and the new remainder 80,and apply the division lemma to get

90 = 80 x 1 + 10

We consider the new divisor 80 and the new remainder 10,and apply the division lemma to get

80 = 10 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 960 and 610 is 10

Notice that 10 = HCF(80,10) = HCF(90,80) = HCF(260,90) = HCF(350,260) = HCF(610,350) = HCF(960,610) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 783 > 10, we apply the division lemma to 783 and 10, to get

783 = 10 x 78 + 3

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 3 and 10, to get

10 = 3 x 3 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 783 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(783,10) .

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Frequently Asked Questions on HCF of 960, 610, 783 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 960, 610, 783?

Answer: HCF of 960, 610, 783 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 960, 610, 783 using Euclid's Algorithm?

Answer: For arbitrary numbers 960, 610, 783 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.